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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 6, Pages 883–889 (Mi zvmmf10701)  

This article is cited in 1 scientific paper (total in 1 paper)

Complexity and approximation of finding the longest vector sum

V. V. Shenmaier

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

Abstract: The problem under study is, given a finite set of vectors in a normed vector space, find a subset which maximizes the norm of the vector sum. For each $\ell_p$ norm, $p\in[1,\infty)$, the problem is proved to have an inapproximability bound in the class of polynomial-time algorithms. For an arbitrary normed space of dimension $O(\log n)$, a randomized polynomial-time approximation scheme is proposed.

Key words: vector sum, finding a vector subset, inapproximability bound, approximation scheme, normed space.

Funding Agency Grant Number
Russian Science Foundation 16-11-10041


DOI: https://doi.org/10.7868/S0044466918060030

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:6, 850–857

Bibliographic databases:

UDC: 519.87
Received: 14.11.2016
Revised: 11.10.2017

Citation: V. V. Shenmaier, “Complexity and approximation of finding the longest vector sum”, Zh. Vychisl. Mat. Mat. Fiz., 58:6 (2018), 883–889; Comput. Math. Math. Phys., 58:6 (2018), 850–857

Citation in format AMSBIB
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\jour Zh. Vychisl. Mat. Mat. Fiz.
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\transl
\jour Comput. Math. Math. Phys.
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\vol 58
\issue 6
\pages 850--857
\crossref{https://doi.org/10.1134/S0965542518060131}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Shenmaier, “Approximability of the problem of finding a vector subset with the longest sum”, J. Appl. Industr. Math., 12:4 (2018), 749–758  mathnet  crossref  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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